The website Snopes is all about this. From debunking urban legends to examining current topical stories, every article is well-researched and has at least a few paragraphs of text. Many of them also go into how the rumor or urban legend started, including just how badly some of the stories have been exaggerated.
Diane Castle from Whateley Universe, writer of the Ayla stories, includes a lot of details that are related to things Ayla should know about. This includes everything from details on restaurants, to discussion of literature. Oh, and lots and lots of business information.
Oh brother. In the latest Aquerna novel, Anna needs to get her squirrels back into hibernation. Someone did a ton of research on which types of squirrels hibernate, and the biochemistry of hibernation, and synthesizing H.I.T., which turns out to be a real chemical that really has been tested and found to induce hibernation in squirrels. It's worked into the story without an infodump, but it's all there.
A number of the authors of the Whateley Universe have done this, from details of computer science to statistical algorithms to a discussion of the physics involved when a PK superboy punches a density-changer who has already gone super-dense.
Stuart Slade, author of The Salvation War and The Big One, is a military statistician and frequently throws in details about weapons, battle strategy, and injuries caused in the battle.
Sometimes this veers into Reality Is Unrealistic territory, as after the USS Normandy (CG-60) incident in Pantheocide (Book 2 of The Salvation War) and the ensuing discussion, he admitted that "I was dancing on the extreme edge of what can be said about SPY-1 and AEGIS in public," referring to the real-life radar and naval combat systems respectively that were used in the story, to the point of handwaving certain statistics as being classified in-universe.
The description of the nuclear warhead on the Gryphon "Glickem" is practically Description Porn that could be mistaken for a blueprint for a nuclear device... good thing some key details are deliberately omitted.
How about the slight mention of the classified "aurora"?
Gametrailers has a tendency to go into insane amounts of research for their "Pop-Up Block" segments, which analyze trailers using context clues. For Assassin's Creed II, for instance, they looked up the names of the masks several characters wore. In English, and the Italian. Would the average user need to know these facts? Probably not, but they're in there anyway.
One of the main characters of The Pains is an electrical engineer. The author uses the correct terminology, in the correct context. Think what you want about the insane "Mindpixel" ramblings later on, but Mr. Sundman's portrayal of circutriy is spot-on.
For all the flak The Other Wiki gets for its "anyone can edit" model, its guidelines call for either extensive footnotes or extensive "" tags. Their "good" and "featured" articles are prime examples of this trope - unless, of course, the article was promoted before the standards for quality articles became so strict.
Out of character, James Rolfe shows a ton of work in his movie reviews. He's especially knowledgeable about the horror genre.
A small group of people on NationStates (mostly comprised of members of NSD—though one does not necessarily mean the other) love to showcase their work in roleplay posts and especially designs. This is taken Up to Eleven in several designs, the Ur-example being the Nakíl, then surpassed by the Lince (it takes up most of that page). If you have time to read all that, I pity you.
The gamemaster ("Serris") of the forum based RP, Darwin's Soldiers apparently does his research when it comes to the sciences. Not to mention weaponry.
46524 This thread shows a lot of effort and research to show that Twilight, no matter what the fans say, and what happens in the book, a lot of the actions in the book are wrong and the Vampires in the series don't even qualify as Vampires, Our Vampires Are Different notwithstanding.
Orion's Arm, extensively, critics of the setting's assumtions are advised to bring a solid familiarity modern science.
Frequently in New York Magician. There's one arc that opens with a detailed account of firefighters fighting a gas fire. Instead of just "they pour water on it", Michel's narration notes the use of foam as a suppressor, and using water mainly to douse any flames that escape the foam. This does beg the question of why a financial guy would even know so much about firefighting, but one can presume he simply looked it up between the end of that story arc and writing it down.
Writer/creator "Curly" Jeffers is a known lover of trivia and academia.
Before every Death Battle, the hosts Wiz and Boomstick give information about the characters that are going to fight; since the main point of the show is to decide the winners with research, this is very important. They even mention lesser known facts like how Starscream possessed a young girl and forgot to pull up her pants after going to the bathroom, or that Batman went back in time and became a pirate. They even use facts to back up predictions like claiming that Pikachu's years of experience makes him level 100 or the speed of Rainbow Dash being Mach 5 or 10 based on her sonic cone before launching a sonic rainboom.
Taken to extremes with the Superman vs. Son Goku battle, where they not only lay out the extreme math given detailing Superman's capabilities (which were outlined in one way or another in Superman media) but also for Goku, who had nowhere near the amount calculations made on part of the creators in the media he has been in. As a result, Wiz and Boomstick had to create formulas to follow in calculating his statistics using what few math Dragonball actually did put into itself to put Goku's capabilities into numbers.
the people behind Die Anstalt really know their psychological theories, from Gestaltzerfall to pathogenetic points of view to theta wave synchronization.
The Nostalgia Critic does a lot of research on movies he reviews. For example, before reviewing Patch Adams, he researched history and work of real Patch Adams, just so he could leash at the movie for how disrespectful for the source material to the point of taking Adams' real life male friend who was murdered, changing him into femaleLove Interest with being molested in childhood as a backstory it is.
Like his character, Doctor Kabalah, writer/player Jason Bennett of the Global Guardians PBEM Universe is an orthodox Jew from New York City, and it shows in Doctor Kabalah's vocabulary, daily actions, magic use, eating habits, sports team affinity, and almost painfully detailed religious observances.
The viral video "Bride Has Massive Hair Wig-Out" had many debating its authenticity (it was staged). One of the arguments in favour of it being real was the bride wearing a button-down blouse - something a bride would wear after getting her hair done for a wedding (so as not to mess up the hair by pulling a top up over it).
Survival of the Fittest encourages this mindset when dealing with any hobbies, medical conditions, laws, or so on during the profile approval process and in the roleplay proper, as to prevent power-playing or handling things in an insensitive manner.
Deconstructs the Connecticut Yankee Plot by pointing out that even an intelligent, well-educated person from the modern age doesn't know enough about how the technology he takes for granted works; he has to basically start from scratch when he finds himself in a low-tech world. Word of God is that it's difficult to give radio to the Romans when you don't know how to build a radio and a radio receiver from first principles, and how many people these days know how to do that?
Horses are not "living cars", but mammals with realistic limits to their physical endurance, making it difficult to cover long distances quickly.
Paul recognizes a sapphire "about half the size of a hen's egg" as an enormous gemstone. Likewise, a piece of solid gold artwork is not only extremely heavy, but also very soft and requires special care when transporting it so it won't get damaged.
Aluminum is considered more valuable than gold. Paul laughs at the concept, saying it's "about as rare as sand" and the real tricky part is separating it from its ores. (Which is very, very difficult unless you have access to electricity, and then it gets a lot easier.) As Paul is conducting research into the generation of electrical power in his spare time, he makes a comment at one point about a long-term plan to develop a process that can generate aluminum in plentiful quantities.
Phooie (the nephew that Scrooge had given to the Beagle Boys before Ducktalez 7) is the fan name given to a fourth nephew that was sometimes mistakenly added into drawings of the Donald Duck comics.
Film Brain does the research about the films he reviews and it shows. This goes to the point that he ends up doing the research where the creators clearly didn't.
In the notorious Seven Pounds, Film Brain points out an absolutely catastrophic research failure on the writer's part: the main character's plan to donate his organs after committing suicide would fail because of his suicide by jellyfish. The jellyfish's venom is cardiotoxic and would damage his heart, rendering it unfit for transplant.
Each of his reviews goes into detail about the production of the film he's reviewing, including the history of the director and writer(s).